When a binary search tree contains duplicate values, the way in-order traversal processes those duplicates depends on the convention used when inserting them into the tree. Typically, a rule is established where duplicate values are consistently placed either in the left or the right subtree of a node. For example, some implementations place duplicates in the right subtree to maintain the invariant that all values in the left subtree are strictly less than the root, and all values in the right subtree are greater than or equal. During in-order traversal, these duplicates will be visited in a way that preserves the chosen insertion order. As a result, the output will still be sorted but may contain repeated values adjacent to each other in the final sequence. The traversal does not treat duplicates specially—it simply follows the structure of the tree. Therefore, careful and consistent handling of duplicates during insertion is crucial to ensure correctness.

In a skewed binary search tree, all nodes are aligned in a single direction—either entirely to the left or entirely to the right—forming a structure similar to a linked list. When performing in-order traversal on such a tree, the traversal process still follows the left → root → right pattern, but because one side is empty at each node, the recursion or iteration proceeds linearly down the single-branch structure. This leads to O(n) time complexity, which is expected, but also to O(n) space complexity due to the depth of recursive calls or the size of the stack in iterative implementations. The key performance implication is that skewed trees do not take advantage of the binary search tree’s intended efficiency, as operations like insertion, searching, and traversal become as inefficient as linear operations. Balancing the tree (e.g. using AVL or Red-Black Trees) is often necessary to maintain optimal traversal performance.

In-order traversal alone cannot reconstruct a binary search tree, because it only reveals the sorted sequence of values from the tree. This sequence lacks structural information about how nodes were arranged in the original tree. Multiple different BSTs can produce the same in-order sequence, particularly when there are no constraints on balance or shape. To reconstruct a BST, additional traversal information is needed—typically a pre-order or post-order traversal used alongside the in-order list. These additional sequences preserve structural relationships, such as which values are roots and subtrees, allowing full reconstruction. Without them, it's impossible to determine the exact hierarchy or branching of the original tree. However, if the task is only to create a BST from a sorted list, a balanced BST can be built by recursively selecting the middle element as the root and constructing left and right subtrees from the respective halves of the list, though this may not match the original tree’s structure.

Yes, in-order traversal can be modified to stop early, typically by introducing a condition within the traversal logic that interrupts the process once a goal is met. For example, during traversal, a search for a particular value can be implemented such that the traversal terminates as soon as the target value is found. This optimisation is useful when the goal is not to traverse the entire tree, but rather to locate or process a subset of the nodes. It can also be applied in range queries, where only values within a specific interval need to be collected. Early termination reduces unnecessary processing and improves efficiency, particularly in large trees. In recursive implementations, this requires returning a signal (such as a boolean) that indicates whether traversal should continue. In iterative implementations, early exits can be managed by breaking out of the loop. This flexibility makes in-order traversal adaptable to many practical scenarios.

In-order traversal plays a critical role in rebalancing an unbalanced binary search tree. The process begins by performing an in-order traversal on the original BST to extract its elements into a sorted list. This step ensures that all values from the tree are preserved in ascending order. Once this sorted list is obtained, the next step is to construct a new, balanced binary search tree from it. This is typically done by recursively choosing the middle element of the list as the root node, then applying the same logic to the left and right halves of the list to build the left and right subtrees. The result is a height-balanced BST, where the difference in height between the left and right subtrees of any node is minimal. This rebalancing improves the time complexity of search, insert, and delete operations by reducing the maximum depth of the tree. In-order traversal is essential in this process because it guarantees sorted order for correct reconstruction.